Ever since the Polish critic, Jan Kott, wrote a famous essay viewing Shakespeare's play as a nightmarish fantasy, directors have been exploring the dark side of The Dream. Michael Grandage's new production – the fourth in his current West End season – takes the opposite tack. Built around the star-power of Sheridan Smith and David Walliams, this is an enormously spirited and fast-moving show that turns into a joyous celebration of sex and fertility.

Occasionally I wished Grandage had dug a little deeper. In the opening scene, Smith's trim-suited Hippolyta looks impassively on as Padraic Delaney's Theseus issues a potential death threat to the mutinous Hermia. You'd have thought an Amazonian queen might have shown a bit more sisterly sympathy for Hermia's plight. Since, as is usual these days, the actors playing Theseus and Hippolyta double as Oberon and Titania, it would also make sense for the quarrel in the fairy kingdom to be foreshadowed in the mortal world.

Once it moves to the forest – dominated, in Christopher Oram's design, by a huge lunar backdrop – the production takes off. The fairies, with their beads, bangles, bandanas and feathers, look as if they've stepped out of a late-60s production of Hair, and their magical powers palpably owe a good deal to uninhibited use of chemical substances. Smith's delightful Titania carries a large spliff, queens it over her followers with fiery independence and seems up for anything: she comes on to the translated Bottom by provocatively thrusting her leg over a balcony rail, and leads him less by the nose than by his extended tail which she caresses with tactile enthusiasm.

In a play all about transformation, one of the production's best internal jokes is the shift that overcomes Walliams's Bottom. As one of the rude mechanicals, he is a campy amateur thesp in a chestnut-coloured Frankie Howerd wig who gleefully paws the breasts of his fellow actor, Francis Flute. Transformed into a buck-toothed, big-eared ass, Walliams turns into a figure of polymorphous sexuality who delights equally in Titania's lascivious embraces and the well-filled honeybag of a hairy fairy. Above all, Walliams has the knack of instinctively connecting with an audience, whether it be in his awed recollection of his donkey's tackle or in his funny play-within-the-play Pyramus who takes the stage with enamelled self-assurance and who is hilariously reluctant to depart.

But what is fascinating is how the woodland quarrel between the quartet of lovers becomes, as so often these days, the highlight of the show. Each production seems to go further than the last; and here there is a riotous mix of passion and pugilism as Susannah Fielding's Hermia first tries to recover the fugitive Lysander by smothering him with kisses and later gets her revenge by a well-aimed kick to the testicles. Even if the two male lovers look oddly similar, it helps that Fielding's spitfire Hermia offers a perfect physical and temperamental contrast to Katherine Kingsley's bewildered, blonde Helena. Both are excellent and remind us that Shakespeare sometimes wrote better for women than for men.

I've suppose I've seen more textually exploratory Dreams, but Grandage's production is sexy, swift and sure-footed, a constant delight to the eye and never lets us forget that this is a play about the magical capacity for change. As Gavin Fowler's Puck spreads his final blessing over the audience, we too feel transported.